We wordlessly prove Apollonius’ theorem.

Apollonius’ theorem, parallelogram identity, Stewart’s theorem, Pythagorean theorem, median

Received: December 9, 2024; Accepted: March 6, 2025; Published: March 20, 2025

How to cite this article: Martin Celli, Proof without words: Apollonius’ theorem (parallelogram identity) via the Pythagorean theorem, Far East Journal of Mathematical Education 27(1) (2025), 17-19. https://doi.org/10.17654/0973563125003

This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License

References:
[1] G. D. C. Stokes, The theorem of Apollonius by dissection, Edinburgh Mathematical Notes 24 (1929), 18. https://doi.org/10.1017/S1757748900001973.
[2] David S. Wise, Proof without words: a generalization from Pythagoras, Mathematics Magazine 71(1) (1998), 64.
https://doi.org/10.1080/0025570X.1998.11996599.